Chapter 7 Permeability and Seepage - Geoengineer.org

1 Permeability and Seepage - N. Sivakugan (2005) 1 Chapter 7 Permeability and Seepage INTRODUCTION Permeability , as the name implies (ability to permeate), is a measure of how easily a fluid can flow through a porous medium. In geotechnical engineering, the porous medium is soils and the fluid is water at ambient temperature. Generally, coarser the soil grains, larger the voids and larger the Permeability . Therefore, gravels are more permeable than silts. Hydraulic conductivity is another term used for Permeability , often in environmental engineering literature. Flow of water through soils is called Seepage . Seepage takes place when there is difference in water levels on the two sides of the structure such as a dam or a sheet pile as shown in Fig. 1. Whenever there is Seepage ( , beneath a concrete dam or a sheet pile), it is often necessary to estimate the quantity of the Seepage , and Permeability becomes the main parameter here. dam sheet pile hL hL Seepage soil Figure Seepage beneath (a) a concrete dam (b) a sheet pile Sheet piles are interlocking walls, made of steel, timber or concrete segments.

2 They are used water front structures and cofferdams (temporary structure made of interlocking sheet piles, making up an impermeable wall surrounding an area, often for construction works as in Fig. 2.) Figure 2. Cofferdam at Montgomery Point Lock, USA (Courtesy: Corps of Engineers 2004) Permeability and Seepage - N. Sivakugan (2005) BERNOULLI S EQUATION h water P z datum Figure Total head at a point Bernoulli s equation in fluid mechanics states that, for steady flow of non-viscous incompressible flow, the total head at a point can be expressed as the summation of three independent components, namely, pressure head, elevation head and velocity head. This is shown in Eq. ( ) 2gp headVelocity headElevation head Pressure head Total2gvzw++=++= where p is the pressure and v is the velocity at a point (P in Fig.)

3 Within the region of flow. The total head and three components in Eq. have the units of length. The second component, elevation head, is measured with respect to an arbitrarily selected datum. It is simply the vertical distance above the horizontal datum line. If the point is below the datum, the elevation head is negative. At point P (Fig. ), the pressure p in Eq. is h wg, and therefore the pressure head is h. FLOW THROUGH SOILS When water flows through soils, whether beneath a concrete dam or a sheet pile, the Seepage velocity is often very small. It is even smaller when squared, and the third component in Eq. becomes negligible compared to the first two components. Therefore, Bernoulli s equation for flow through soils becomes: ( ) gp headElevation head Pressure head Totalzw+=+= Neglect the velocity head in flow through soils.

4 When water flows through soils, from upstream to downstream, due to difference in water level as in Fig. , some energy is lost in overcoming the resistance provided by the soils. This loss of energy, expressed as total head loss (hL), is simply the difference in water levels. The pressure p is the pore water pressure (u), and therefore pore water pressure at any point in the flow region can be written as: ( ) head Prwgessureu = Permeability and Seepage - N. Sivakugan (2005) 3In Fig. , if h = 3 m, the pressure head and pore water pressure at P are 3 m and kPa respectively. A B Figure Hydraulic gradient Hydraulic gradient is the total head loss per unit length. When water flows from point A to point B as shown in Fig. , the total head at A has to be greater than that at B. The average hydraulic gradient between A and B, is the total head lost between A and B divided by the length AB along the flow path.

5 ( ) ABlength Bat head Total -A at head Total= BAi The hydraulic gradient is a constant in a homogeneous soil, since it is a measure of the head loss per unit length. It is dimensionless. If the soil is not homogeneous, the hydraulic gradient can vary from point to point. EXAMPLE 300 mm 900 mm 400 mm 300 mm ABX Figure A 900 mm long cylindrical soil sample, contained as shown in Fig. , is subjected to a steady state flow under constant head. Find the pore water pressure at a point X. Solution: Let s take the tail-water level as the datum. Permeability and Seepage - N. Sivakugan (2005) 4 Total head loss across the specimen is 1600 mm. average hydraulic gradient within the soil = 1600/900 = Total head at A = 1600 mm For the flow from A to X, A to fromlength Xat head Total -A at head Total= head Total - 1600= Total head at X = mm Elevation head at X = mm Pressure head at X = mm Pore water pressure at X = -( )( ) = kPa In Seepage problems I generally select the tail water or downstream water level as the datum.

6 The choice of datum can only affect the elevation and total head, but not the pressure head or the pore water pressure. DARCY S LAW In 1856, a French engineer Darcy proposed that, what the flow through soils is laminar, the discharge velocity (v) is proportional to the hydraulic gradient (i). Darcy s law is thus: v i v = k i ( ) Here, the constant k is known as the coefficient of Permeability or simply Permeability . It is also called hydraulic conductivity. Since i is dimensionless, k has the unit of velocity. In geotechnical engineering k is commonly expressed in cm/s (although m/s is the preferred metric unit), and other possible units include m/s, m/day, and mm/hour. In mining engineering, mm/hour is the preferred unit for Permeability of mine fills and bricks. In coarse grained soils, the effective grain size D10 has good correlation with Permeability .

7 Hazen (1911) suggested that, for uniform sands (Cu < 5) having D10 of mm, in its loosest state, k and D10 are related by: k (cm/s) = D102 (cm) ( ) There have been attempts to correlate Permeability with e2, e2/1+e, e3/1+e. One can intuitively see that larger the D10 or e, larger the void volume and thus larger the Permeability . Typical Permeability values for the common soil types, and what these mean when it comes to drainage characteristics, are summarized in Table (Terzaghi et al. 1996). When k is less that 10-6 cm/s, the soil is practically impervious. Permeability and Seepage - N. Sivakugan (2005) 5 Table Permeability and drainage characteristics of soils (Terzaghi et al. 1996) Very fine sands, organic & inorganic silts, mixtures of sand silt & clay, glacial till, stratified clay deposits, etc. Impervious soils modified by effects of vegetation&weatheringClean sands, clean s& gravel mixtures and Clean gravel Impervious soils , homogeneous clays below zone of weathering Practically imperviousPoorGood Soil Types Drainage 10-810-910-1010-710-1110-310-210-410-610 -5 Permeability (m/s) 10-1100 It is good to have an idea about the order of magnitude for the Permeability of a specific soil type.

8 LABORATORY DETERMINATION OF Permeability Permeability of a coarse grained soil can be determined by a constant head Permeability test ( ; ASTM D2434), and in a fine grained soil, falling head Permeability test ( ; ASTM D5856) works the best. In a constant head Permeability test (Fig. ), the total head loss (hL) across a cylindrical soil specimen of length L and cross sectional area A, is maintained constant throughout the test, and at steady state, the flow rate (Q) is measured. L A L hLmeasuring cylinder Figure Constant head Permeability test Therefore, the discharge velocity (v) is given by: v = Q/A Permeability and Seepage - N. Sivakugan (2005) 6 The hydraulic gradient (i) across the soil specimen is hL/L. Applying Darcy s law, Q/A = k hL/L Therefore, k is given by: ( ) AhQLkL= Why can t we do constant head Permeability test on fine grained soils? It just takes quite a long time to collect a measurable quantity of water to compute the flow rate.

9 A simplified schematic diagram for a falling head Permeability setup is shown in Fig. The cylindrical soil specimen has cross sectional area of A and length L. The standpipe has internal cross sectional area of a. Figure Schematic diagram of a falling head Permeability test setup h L By applying Darcy s law, and equating the flow rate in the standpipe and the soil specimen, it can be shown that the Permeability can be computed from Eq. ( ) ln21 =hhAtaLk Permeability and Seepage - N. Sivakugan (2005) 7 Here, t is the time taken for the water level in the standpipe to fall from h1 to h2. Why can t we do falling head Permeability test on coarse grained soils? The flow rate is so high that water level will drop from h1 to h2 within a few seconds, not giving us enough time to take the measurements properly. Permeability in the field can be measured through a pump-in or pump-out test on a well or bore hole.

10 Here, the flow rate to maintain the water table at a specific height is measured and the Permeability can be computed using some analytical expressions found in textbooks. STRESSES IN SOILS DUE TO FLOW X hwz L X hwz L L hwX z hLhL(a) (b) (c) Figure Three different scenarios (a) Static (b) Flow-up (c) Flow-down Three different scenarios, of identical soil specimens subjected to different flow conditions, are shown in Fig. In Fig. a, there is no flow and the water is static. In Figs. b, flow takes place due to a head difference of hL across the specimen, and the flow is upwards through the specimen. In Fig. c, the flow through the specimen is downwards, again due to a head difference of hL. When there is flow, the hydraulic gradient i is given by hL/L.